Q. 18 B5.0( 3 Votes )

If 15 cot A=18, find sin A and sec A.

Answer :

Given: 15 cot A = 8



And we know that,



Or



Let,


Side adjacent to angle A =AB = 8k


The side opposite to angle A =BC = 15k


where k is any positive integer


Firstly we have to find the value of AC.


So, we can find the value of AC with the help of Pythagoras theorem


(AB)2 + (BC)2 = (AC)2


(8k)2 + (15k)2 = (AC)2


(AC)2 = 64 k2 +225 k2


(AC)2 = 289 k2


AC =289 k2


AC =±17k


But side AC can’t be negative. So, AC = 17k


Now, we will find the sin θ



Side opposite to angle θ = BC = 15k


and Hypotenuse = AC = 17k


So,


Now, we know that,



The side adjacent to angle θ = AB =8


Hypotenuse = AC =17


So,





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